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11
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Recent Developments in Finite Element Methods for Structural Acoustics
, 1996
"... This paper reviews recent progress in finite element analysis that renders computation a practical tool for solving problems of structural acoustics ..."
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Cited by 14 (3 self)
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This paper reviews recent progress in finite element analysis that renders computation a practical tool for solving problems of structural acoustics
Midfrequency vibroacoustic modelling: challenges and potential solutions
 In Proceedings of ISMA 2002
, 2002
"... At present, the main numerical modelling techniques for acoustic and (coupled) vibroacoustic analysis are based on element based techniques, such as the finite element and boundary element method. Due to the huge computational efforts, the use of these deterministic techniques is practically restri ..."
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Cited by 10 (5 self)
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At present, the main numerical modelling techniques for acoustic and (coupled) vibroacoustic analysis are based on element based techniques, such as the finite element and boundary element method. Due to the huge computational efforts, the use of these deterministic techniques is practically restricted to lowfrequency applications. For highfrequency modelling, some alternative, probabilistic techniques such as SEA have been developed. However, there is still a wide midfrequency range, for which no adequate and mature prediction techniques are available at the moment. In this frequency range, the computational efforts of conventional element based techniques become prohibitively large, while the basic assumptions of the probabilistic techniques are not yet valid. In recent years, a vast amount of research has been initiated in a quest for an adequate solution for the current midfrequency problem. This paper discusses the various methodologies that are being explored in this perspective. The main focus of this paper lies on the methodology that looks for deterministic techniques with an enhanced convergence rate and computational efficiency compared to the conventional element based methods in order to shift the practical frequency limitation towards the midfrequency range. In this respect, special attention is paid to the wave based prediction technique for (coupled) vibroacoustic analysis that is being developed at the KULeuven Noise and Vibration Research group. The method is based on an indirect Trefftz approach. Various recent validations have revealed the beneficial convergence rate of this novel technique, thereby exhibiting its potential to comply with the midfrequency modelling challenge. 1.
The Influence of the Mass Matrix on the Dispersive Nature of the SemiDiscrete, SecondOrder Wave Equation
, 1998
"... The application of discrete solution methods to the secondorder wave equation can yield a dispersive representation of the nondispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of pr ..."
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Cited by 7 (2 self)
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The application of discrete solution methods to the secondorder wave equation can yield a dispersive representation of the nondispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation. In this work, the dependence of the dispersive errors on the wave propagation direction, mesh aspect ratio, and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the twodimensional bilinear finite element. An analysis of the dispersive effects associated with the consistent, rowsum lumped and higherorder mass matrices has led to a reducedcoupling "pentadiagonal" mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction. The influence of rowsum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group er...
Results of von Neumann Analyses for Reproducing Kernel Semidiscretizations
, 1998
"... The Reproducing Kernel Particle Method (RKPM) has many attractive properties that make it ideal for treating a broad class of physical problems. RKPM may be implemented in a "meshfull" or a "meshfree" manner and provides the ability to tune the method, via the selection of ..."
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Cited by 6 (3 self)
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The Reproducing Kernel Particle Method (RKPM) has many attractive properties that make it ideal for treating a broad class of physical problems. RKPM may be implemented in a "meshfull" or a "meshfree" manner and provides the ability to tune the method, via the selection of a window function and its associated dilation parameter, in order to achieve the requisite numerical performance. RKPM also provides a framework for performing hierarchical computations making it an ideal candidate for simulating multiscale problems. Although the method has many appealing attributes, it is quite new and its numerical performance is still being quantified with respect to more traditional discretization techniques. In order to assess the numerical performance of RKPM, detailed studies of the method on a series of model partial differential equations has been undertaken. The results of von Neumann analyses for RKPM semidiscretizations of one and twodimensional, first and secondorder ...
Dispersion analysis of stabilized finite element methods for acoustic fluid interaction with Reissner–Mindlin plates
 Int J Numer Meth Eng
"... The application of stabilized finite element methods to model the vibration of elastic plates coupled with an acoustic fluid medium is considered. New stabilized methods based on the HellingerReissner variational principle with a generalized leastsquares modification are developed which yield impr ..."
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Cited by 6 (3 self)
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The application of stabilized finite element methods to model the vibration of elastic plates coupled with an acoustic fluid medium is considered. New stabilized methods based on the HellingerReissner variational principle with a generalized leastsquares modification are developed which yield improvement in accuracy over the Galerkin and Galerkin Generalized Least Squares (GGLS) finite element methods for both in vacuo and acoustic fluidloaded ReissnerMindlin plates. Through judicious selection of design parameters this formulation provides a consistent framework for enhancing the accuracy of mixed ReissnerMindlin plate elements. Combined with stabilization methods for the acoustic fluid, the method presents a new framework for accurate modeling of acoustic fluidloaded structures. The technique of complex wavenumber dispersion analysis is used to examine the accuracy of the discretized system in the representation of freewaves for fluidloaded plates. The influence of different finite element approximations for the fluidloaded plate system are examined and clarified. Improved methods are designed such that the finite element dispersion relations closely match each branch of the complex wavenumber loci for fluidloaded plates. Comparisons of finite element dispersion relations demonstrate the superiority of the hybrid leastsquares (HLS) plate elements combined with stabilized methods for the fluid over standard Galerkin methods with mixed interpolation and shear projection (MITC4) and GGLS methods. Corresponding author.
Complex WaveNumber Dispersion Analysis Of Stabilized Finite Element Methods For Acoustic Fluid  Structure Interaction
"... The application of nite element methods to problems in structural acoustics ( the vibration of an elastic body coupled to an acoustic uid medium) is considered. New stabilized methods based on the HellingerReissner variational principle with a generalized leastsquares modication are developed whic ..."
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Cited by 1 (1 self)
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The application of nite element methods to problems in structural acoustics ( the vibration of an elastic body coupled to an acoustic uid medium) is considered. New stabilized methods based on the HellingerReissner variational principle with a generalized leastsquares modication are developed which yield improvement in accuracy over the standard Galerkin  nite element method for both in vacuo and acoustic uidloaded ReissnerMindlin plates. Through judicious selection of design parameters this formulation provides a consistent framework for enhancing the accuracy of mixed ReissnerMindlin plate elements that have no shear locking or spurious modes. Combined with Galerkin LeastSquares (GLS) methods for the acoustic uid, the method presents a new framework for accurate modeling of acoustic uidloaded structures. The technique of complex wavenumber dispersion analysis is used to examine the accuracy of the discretized system in the representation of freewaves for uidloaded plates. ...
Generalized Fourier analyses of the advectiondiffusion equation – Part I: onedimensional domains
 Int. J. Numer. Methods in Fluids
"... This paper is focused on a detailed multimethods comparison of the spatial errors associated with finite difference, finite element and finite volume semidiscretizations of the scalar advectiondiffusion equation. The errors are reported in terms of nondimensional phase and group speed, discrete ..."
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Cited by 1 (0 self)
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This paper is focused on a detailed multimethods comparison of the spatial errors associated with finite difference, finite element and finite volume semidiscretizations of the scalar advectiondiffusion equation. The errors are reported in terms of nondimensional phase and group speed, discrete diffusivity, artificial diffusivity, and gridinduced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the spectral behavior of the discrete advective operator into its symmetric and skewsymmetric components. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind PetrovGalerkin and its controlvolume finite element analogue, the streamline upwind controlvolume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semidiscrete artifacts observed in the discrete phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit superconvergent behavior in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly secondorder behavior. In Part I1 of this paper, we consider twodimensional semidiscretizations of the advectiondiffusion equation
Finite Element Formulation for a Baffled, FluidLoaded, Finite Cylindrical Shell
"... A new method for obtaining the response of a baffled, fluidloaded, finite cylindrical shell using the finite element method is presented. The Galerkin finite element formulation for this problem utilizes a Neumann Green's function representation of the pressure loading on the shell. By repres ..."
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A new method for obtaining the response of a baffled, fluidloaded, finite cylindrical shell using the finite element method is presented. The Galerkin finite element formulation for this problem utilizes a Neumann Green's function representation of the pressure loading on the shell. By representing the pressure loading in this manner, only the structure need be discretized. Both C 0 and C 1 finite element discretizations of the shell are considered. The finite element results are compared to analytic solutions of the fluidloaded cylinder which are obtained using an expansion of the displacement in terms of the in vacuo modes of the NaghdiCooper and Flugge shell theories. 1. Introduction A finite element formulation for the vibration of a baffled, fluidloaded, finite cylindrical shell is developed. The geometry consists of a finite cylindrical shell embedded between two rigid semiinfinite cylindrical baffles immersed in an unbounded acoustic medium, see Fig. 1. This geome...
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"... a b s t r a c t For optimization problems based on dynamic criteria the system eigenvalues must be recomputed for each iteration as the values o f the design parameters are changed. From a computational point of view it would be more efficient to replace the laborious process o f determining the ei ..."
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a b s t r a c t For optimization problems based on dynamic criteria the system eigenvalues must be recomputed for each iteration as the values o f the design parameters are changed. From a computational point of view it would be more efficient to replace the laborious process o f determining the eigenvalues by direct prediction. The suitability and advantages o f this scheme are examined here. The number o f operations required by the direct and the predictive solution algorithms are compared. The prediction scheme has been applied to the problem o f maximizing the separation o f two adjacent eigenvalues for structural and couple fluidstructure systems. s o m m a ir e Les problèmes d ’optimisation basés sur des critères dynamiques doivent obtenir les valeurs propres de système, qui dépendent directement des valeurs des variables de conception. Pendant le processus d ’optimisation la fonction objective est calculée à plusieurs reprises pour chacun nouvel ensemble de variables de conception, et alors une alternative plus économique du point de vue informatique devrait prévoir les valeurs propres pour le nouvel ensemble de variables au lieu de résoudre le problème encore. Ainsi, le but de ce travail est de déterminer la convenance et les avantages d ’employer la prévision de valeurs propres, au lieu des solutions directes, dans les itérations pendant le processus d ’optimisation. Puis, le nombre d ’opérations entre